Internal Load, External Load and the Pole Efficiency Index (PEI) in Cross-Country Skiing

Dan Kuylenstierna — 2025-05-01

There are several ways to measure the load the body is exposed to during physical exertion. These can be divided into measures of internal load and external load. Internal load refers to how hard the body is working, while external load refers to the work the body is performing.

Examples of metrics that reflect the body’s internal load include heart rate, lactate, and oxygen uptake (VO2). Of these, VO2 is also a measure of capacity (work ability). Even though VO2 indicates work capacity, it is not a direct measure of performance. To compare performance, we need a measure of external load. The best measure of external load is work per unit of time — that is, power (watts). Power is proportional to VO2 through the body’s efficiency. Simply put, external power can be increased either by raising internal work capacity (VO2) or by increasing efficiency.

How Skisens Measures Power

Skisens power is based on measuring pole force and multiplying it by speed. Because the pole force axis is not aligned with the direction of travel, we also apply a factor called the Poling Efficiency Index (PEI), defined as the ratio between force in the direction of travel and the pole axis force. In practice, PEI is not known at the individual level and is set to a constant value of PEI = 0.6 in the Skisens interface — a typical value for a trained skier skiing at controlled speed on light terrain. This is, of course, an approximation. In reality, PEI varies with technique and intensity, which means that Skisens power does not fully overlap with external power as measured in cycling.

Because Skisens power does not directly correspond to external power, we need to think differently about data interpretation compared to cycling. A skier showing higher Skisens power is not automatically a better skier. One contributing factor to high Skisens power may be a lower PEI. However, Skisens power has been shown to correlate extremely well with internal load—better than external power, which in skiing is highly dependent on incline versus flat terrain.

Example: Constant External Power

Figure 1 shows Skisens power overlaid with speed for a skier on a treadmill holding a constant external power of 200 watts across different combinations of speed and incline. Notice how heart rate is higher when Skisens power is higher, even though external power is the same. To exclude accumulated fatigue, the test was conducted in both directions—first starting at high speed (Figure 1a), then low speed (Figure 1b). In both cases, it is clear that both heart rate and Skisens power depend on speed. Both increase at high speed, with a tendency to increase in steeper incline, creating a “sweet spot” where Skisens power is lowest.

The variations in Skisens power seen in Figure 1 can be translated into variations in PEI. This is illustrated in Figure 2, which also shows the protocol of varying speed and incline. Behind these variations are technique differences, reflected in Skisens key metrics: impulse, frequency, and contact time, shown in Figure 3.

Modeling the Pole Efficiency Index

Figure 3 shows that speed correlates strongly with contact time and therefore PEI also correlates with contact time, allowing extraction of a model. Empirically, the model in Equation (1) fits well when modeling PEI as a function of contact time, as shown in Figure 3(b).

Figure 4 shows the model applied to PEI across the test. By applying the model to Skisens power, it becomes possible to estimate external power. Figure 5 shows estimated external power, which—unlike Skisens power—fluctuates around a constant value during the test.

Interval Example

Figure 6 shows data from an interval session on a treadmill. Notice how Skisens power is lower than external power but correlates strongly with it—indicating PEI > 0.6 and modest variation across speed.

Discussion and Conclusions

In this text, we discussed interpretation of Skisens power compared to power interpretation in cycling. First, both are measures of load. At an individual level, one can work similarly—using FTP expressed in Skisens power to guide intervals. For more detailed control of high-intensity intervals, one can use a power profile.

However, when comparing performance, we must think differently. Skisens power is not the same as external power, as in cycling. The reason is variation in the pole efficiency index —the share of force directed forward—between skiers. Those who want to understand their PEI more precisely can run a treadmill protocol and model how PEI varies with speed and contact time. Based on such a model, it becomes possible to calculate external power—a direct performance metric, just as in cycling.